Proc. of Microelectronics & Nanotechnology (2014) Received 2 July 2013; accepted 7 October 2013

1

Cardiac Excitation-Conduction Modeling using

MATLAB/Simulink for Real Time FPGA Implementation

Nur Atiqah Binti Adon1, Farhanahani Binti Mahmud2

1 2 Department of Electronic Engineering,

Faculty of Electric and Electrical Engineering, Universiti Tun Hussein Onn Malaysia,

86400 Parit Raja, Batu Pahat, Johor, MALAYSIA.

1. Introduction Electrical excitations of cardiac cell membranes

and their propagation in the heart tissue control the

mechanical contractions of the cells through the cardiac

excitation-contraction (E-C) coupling mechanism, leading to coordinated contractions of the heart to pump

blood. The excitation event is finely controlled by

influx and efflux of transmembrane currents through

various types of ion channels permeable to specific

kinds of ions. Cardiac excitation involves generation of

the action potential (AP) by individual cells and its

conduction from cell-to-cell through intercellular gap

junctions. The cardiac excitation can be characterized

by an AP, where the AP is generally has five phases. In

general terms, excitation of a cardiac cell is brought

about by the change in potential across the cell

membrane, due to transmembrane fluxes of various

charged ions (𝑁𝑎+, 𝐾+,𝐶𝑎2+, 𝐶𝑙−, etc) [1]. In a normal dynamics of the heart, the electrical

excitation wave dies when it reaches a complete

activation of myocardium because of a refractoriness

effect of the cardiac tissue that has excited before.

Although most hearts can disrupt the mechanical

functioning of the heart, disturbing the coordinated

contraction of the myocardium and preventing the heart

from supplying sufficient blood to the body. This is

known as a cardiac arrhythmia. Arrhythmias caused by

abnormalities in conduction are often the result of

reentrant excitation. Reentry occurs when previously

activated tissue is repeatedly activated by the

propagating AP wave as it reenters the same anatomical

region and reactivates it. Reactivation occurs

indefinitely until the excitability of the tissue in the

reentrant circuit somehow affected [2].

In recent years, experimental researches and clinical purposes on the membrane potential and the AP

have made it possible to reveal the underlying

mechanisms in the electrical state of the heart.

Although both of studies mechanisms are generally

preferable, investigating the cardiac electrical behavior

experimentally poses a number of challenges, such as a

limitation on quantity of variables for monitoring or

deprivation of high-resolution data in investigating

larger preparations [3]. On the other hand,

mathematical modeling techniques for a computer

simulation of cardiac electrical behavior are not associated with such complications.

The mathematical modeling in excitable media is

pioneered by Hodgkin and Huxley, who formulated a

mathematical description of AP generation in the giant

Abstract: The paper will discuss the development of an FPGA-based implementation of hardware model for the

electrical excitation of a cardiac cell based on FitzHugh-Nagumo (FHN) mathematical model. The FHN model is described by a set of nonlinear Ordinary Differential Equations (ODEs) that include two dynamic state variables for

describing the excitation and the recovery states of a cardiac cell and the model is able to reproduce many

characteristics of electrical excitation in cardiac tissues. The electrical excitation of the cells and their propagation in

the heart tissue provides a basic of the physiological function of the heart through the cardiac excitation-contraction

(E-C) mechanism. One way to understand normal and abnormal dynamics of the heart is to develop a

comprehensive mathematical model of the cardiac excitation in order to study underlying mechanisms of the heart

electrical system. However, simulating the dynamics of large numbers of cellular models forming a tissue model

requires an immense amount of computational time. Our intention in this present study is to perform real-time

simulations of the cellular excitations of the cell models using Field Programmable Gate Array (FPGA) to design a

hardware model responsible for the cellular excitations in tissue level. MATLAB models can be used for hardware

design by using HDL Coder for HDL code generation. HDL Coder automates the algorithm design process, from modeling to FPGA implementation.

Keyword: FPGA-implemented hardware model, FitzHugh-Nagumo Model

Proc. of Microelectronics & Nanotechnology (2014)

2

squid axon in 1952 [4]. In the cardiac cell, starting from

the electrical excitation model of the FitzHugh-Nagumo

(FHN) model [5], the Noble Purkinje model [6], the

Beeler and Reuter [7], the Luo-Rudy ventricular model

[8, 9, 10] have been developed to represent different

regions of the heart. With the progress of technology, the computational techniques become more advance but

complicated as variables parameters in the

mathematical descriptions are increased in order to

represent the cellular processes in more detail. Thus,

tissue models consisting of a large number of single cell

models cause a drawback in the amount of

computations for the dynamic simulations of the

mechanism.

To overcome have the computational challenge,

there are studies of hardware-implemented for electrical

excitation modeling that provides valuable tools for

real-time simulations [11-19]. However, only a few studies have succeeded to design analog circuits that are

biophysically detailed and have quantitative

correspondence to a real cell. A previous study from

Farhanahani et al. [20] have provided the analog-digital

circuits of hardware-implemented cardiac excitation

model designed by using analog circuits and a dsPIC

microcontroller that could reproduce a real-time

simulation of Luo-Rudy based cardiac AP model.

However, the hybrid cell models have shown

limitations due to their power consumption and the less

suitable of the dsPIC to perform rapid calculations in performing the real-time operation.

Thus, study of an Field Programmable Gate Array

(FPGA) implemented real-time cardiac excitation

modeling will be carried out in order to solve these

problems as it is suitable for real-time applications and

has low power consumption [21]. Currently, the FPGA

technology has been advanced enough to model

complex chips with the realistic operating frequency.

Reconfigurable hardware modeling, in the form FPGAs

appears of high performance systems at an economical

price [22].

Consequently, FPGAs seem an ideal candidate to utilize and exploit their inherent advantages such as

special low power consumption, millions of bit-level

operations and extremely sophisticated tools to be used

in this time [23]. Here, we focus on the FHN model, the

Ordinary Differential Equation (ODE) model of cardiac

cell for the AP generation in a mammalian cardiac

ventricle. In this study, HDL Coder in MATLAB will

be used to automate the algorithm design process, from

modeling to FPGA implementation.

The rest of the paper is organized as follows. In

Sec. 2, numerical model of FHN which is the base method in developing the model is explained. In Sec. 3,

details on a method of a cable model in performing the

AP conduction are described. In Sec. 4 details of

method for HDL Code generation from Simulink and

MATLAB code are described. In Sec. 5, result and

analysis were discussed from the numerical simulation

of the FHN model. Summary of the paper is lastly

inferred in Sec. 6.

2. FitzHugh-Nagumo (FHN) Model Many models have been proposed to simulate the

cardiac action potential (AP). Numerical models of

cardiac cell are widely used related with reentrant

arrhythmia to investigate the underlying dynamics of

reentrant wave. Basically, these electrophysiology of

isolated cardiac cell models are coupled together to

perform simulations of AP propagation in the cardiac tissue.

FHN equations are a simplified version of the

Hodgkin-Huxley (HH) model that, presents some of the

essential features of HH’s equations and it is more

convenient for a controller design process [24]. The

FHN model can be used to model the cardiac cells

transmembrane potential. Each cell in the heart

conduction system has an individual set of parameters

with a specific AP representing the cell location and

role within the cardiac structure.

Equations (1) and (2) show the ODEs for the FHN model to simulate the AP.

𝜕𝑉

𝜕𝑡= −𝑉(𝑉 − 0.139)(𝑉 − 1) − 𝑊 + 𝐼 + 𝐷

𝜕2𝑉

𝜕𝑥2 (1)

𝜕𝑊

𝜕𝑡= 0.008(𝑉 − 2.54𝑊) (2)

Here, V is a membrane voltage, W is a refractory period,

D is a diffusion coefficient, I is a time and space

dependent injected current [25].

3. An Active Circuit Cable Model Cardiac contraction is initiated by propagating

electrical waves of excitation. The spread of excitation

in the heart occurs due to excitability of individual

cardiac cells and due to close electrical coupling of

cardiac cells via gap junctions, thereby allowing propagation of these electrical excitations from cell to

cell in tissue [26]. Propagation of action potentials in an

excitable tissue is often modeled by using significantly

simplified quantitative method that can be represented

by the one dimensional (1D) cable model. To describe

wave propagation in cardiac tissue, it is necessary to

specify the currents resulting from the intercellular

coupling, which can usually be approximated by a

differential in equation (3).

𝜕𝑉𝑚

𝜕𝑡= 𝐷(𝛻2𝑉𝑚) −

𝐼𝑚

𝐶𝑚

(3)

Proc. of Microelectronics & Nanotechnology (2014)

3

Where 𝑉𝑚 is the cardiac cell membrane voltage, 𝐷 is

the conductivity tensor, 𝐶𝑚 is the membrane

capacitance and 𝐼𝑚 is transmembrane ionic current

specified by FHN model. According this equation, the cable model of the 1D

ring consists of N cell models can be illustrated as

shown Fig. 1, where a gap junction resistance, R is

corresponded to 1/D. In this study, the cable model of

the 1D ring with a gap junction resistance of R =

0.5kΩcm2 which is equaled to D = 2cm2/sec. The

applied value of R is considered relevant as it belongs

to the range that provides a moderate coupling and

allows a propagation of the action potential (AP).

Fig. 1 A ring-shaped active cable model. The ring

model consists of N cell models and gap junction resistance, R.

4. Methods for HDL Code Generation Programmable devices Field Programmable Gate

Arrays (FPGAs) are very important part of the

development process for almost every electronic system.

FPGA gives resources that can be configured to implement variety of arithmetic and logical functions.

Nowadays, model based development is common

practice with a wide range of specialized software tools

for modeling and simulation such as Simulink and

MATLAB code are used for designing, implementing,

and checking the functionality of new controller

functions. The quality and efficiency of the software are

strongly dependent upon the quality of the model used for

code generation.

The model based design with Simulink and

MATLAB code gives an opportunity for obtaining hardware descriptions without handwriting of Hardware

Description Language (HDL) code and by using an

automatic code generation process [27]. This can be done

by HDL Coder that supports code generation.

There are many architectures and implementation

processes made by different software packages such as

Xilinx ISE Project Navigator. This software package

gives a convenient way for simulation of different system

descriptions and synthesis of electronic systems which are

described with HDL. The two most popular HDLs are

VHDL and Verilog. The simple flow design as shown in

Fig. 2.

In addition, FPGA and Application Specific

Integrated Circuit (ASIC) designs can be used for HDL

Coder and HDL Verifier to specify and explore functional

behavior, generate HDL code for implementation, and continuously test and verify your design through co-

simulation with HDL simulators or FPGA-in-the-loop.

Fig. 2 FPGA and ASIC design with HDL Coder and

HDL Verifier.

4.1 HDL Code Generation for Simulink Simulink HDL Coder automates the algorithm design

process, from modeling to FPGA implementation.

Simulink HDL Coder can control HDL architecture,

implementation and generate hardware resource utilization reports. For automatic generation of hardware

description and FPGA implementation the model have to

be realized with blocks from the library hdlsupported.

HDL code generation process starts by modeling the

algorithm in Simulink more than 200 blocks. This library

provides complex functions, such as the Fast Fourier

Transform (FFT), Cascaded Integrator Comb (CIC)

filters, and Finite Impulse Response (FIR) filters. Finally,

to model the signal processing and communications

systems and generating HDL code.

4.2 HDL Code Generation for MATLAB

code The HDL Coder automatically converts MATLAB

code from floating-point to fixed-point and generates

synthesizable VHDL and Verilog code. This capability

lets algorithm at a high level using abstract MATLAB

constructs and system objects while providing options for

generating HDL code that is optimized for hardware

implementation. The process of translating MATLAB

designs to hardware consists of the several steps involves

model the algorithm in MATLAB, generate HDL code,

verify HDL code and create and verify FPGA prototype.

Proc. of Microelectronics & Nanotechnology (2014)

4

5. Results And Analysis

5.1 Simulink Method

The FHN model of an action potential (AP)

generation has been built by blocks from the Simulink

library. The model for a single cell is shown in Fig. 3.

Fig. 3 The FHN model of single cell in Simulink model.

The AP and the recovery state waveforms of single

cell produced by the FHN model are shown in the Fig. 4.

The waveform of membrane potential and recovery

variable varying against time by the FHN model based numerical cardiac excitation in single cell are as shown in

Fig. 4(a) and Fig. 4(b), respectively.

(a)

(b)

Fig. 4 The AP and recovery state waveforms of single cell

produced by the FHN model. (a) and (b) represent the

time variance of membrane potential and the time

variance of recovery variable, respectively.

The AP conduction model of three FHN cells

connected in 1D ring cable model has also been built

using the Simulink as shown in Fig. 5.

Fig. 5 Three membrane cells in Simulink model.

Proc. of Microelectronics & Nanotechnology (2014)

5

The AP and recovery state waveforms of three FHN

cells connected in 1D ring cable model is shown in the

Fig. 6. The AP conduction around the closed ring active

circuit cable consists of three FHN cell models has been

performed. The waveforms overlapped because of the

small value diffusion coefficient.

(a)

(b)

Fig. 6 The AP and recovery state waveforms of three

FHN cells connected in 1D ring cable model. (a) and (b)

represent the time variance of membrane potential and the

time variance of recovery variable, respectively.

5.2 MATLAB code method In this project, a simulation of an anatomical circus

reentry around the closed ring cable consists of eighty

cells of the FHN model has been performed. It is known

that the reentry occurs because the present of

unidirectional conduction block of conducting action

potentials and excitable gap. Unidirectional block occurs

when an action potential (AP) wave-front fails to

propagate in one particular direction, but can continue to propagate in other directions. Here an unidirectional block

was induced by using the so called S1-S2 protocol [28]

where single or several impulsive stimulations referred to

as S1 were applied at a given location of the ring, and

then another impulsive stimulation referred to as S2 was

applied at a different location from the S1 site in a

particular time.

As shown in Fig. 7, two S1 stimulations were applied

to the ring at the first cell at time t = 100 ms and t = 250

ms, pacing the excitation of the medium. Each stimulus

evokes excitation at the stimulated site, generating two

conducting action potentials. The S2, corresponding to an

ectopic focus excitation in the real heart, was then applied

at a position slightly away from the S1 site at an

appropriate time interval after the second application of

S1. For the result, S2 was applied at the fifteenth cell at t = 460 ms, where the time interval of S1 and S2 was 110

ms after the S1 stimulation. Since the action potentials

generated by the S1 were annihilated eventually, the

single AP generated by the S2 alone was left, initiating

the circus movement reentrant wave. According to the

result, after around 1070 ms of reentrant propagation, S3

stimulation was applied at the fifteenth cell caused the

termination of the reentrant wave.

Fig. 7 A space-time diagram showing membrane

voltage as a function of time and position around the

ring-shaped cable presented by numerical model of the

FHN.

6. Summary This paper described a Simulink model and

MATLAB code can be automated from modeling to Field

Programmable Gate Array (FPGA) implementation using

HDL Coder. The coder generates VHDL or Verilog code

that implements the design embodied in the model. In this

paper, the simulations of cardiac action potential (AP) and

conduction based on the FHN model using the Simulink

blocks and MATLAB scripts have been carried out. The

simulation of the reentrant propagation of the FHN cells

in 1D ring-shaped cable model also has been performed.

From this study, we are concerned that the implementation for real time cardiac excitation modeling

using FPGA/MATLAB could be one of alternative tools

far better understanding the mechanisms of reentry.

Proc. of Microelectronics & Nanotechnology (2014)

6

Acknowledgement This research is supported by the Fundamental

Research Grant Scheme (FRGS) by Universiti Tun

Hussein Onn Malaysia (vote no. 1053), UTHM. The

author gratefully acknowledges the support and advice of

Dr. Farhanahani Binti Mahmud, UTHM.

References [1] Nash M.P. and Panfilov A.V. Electromechanical

Model of Excitable Tissue to Study Reentrant

Cardiac Arrhythmias. Biophysics and Molecular

Biology, Vol 85 (2004): 501–522.

[2] Mark T.K. and Michael C.S. Molecular and Cellular

Mechanisms of Cardiac Arrhythmias. Cell Press,

Vol 104 (February 2001): 569–580.

[3] Mahmud F. Real-Time Simulation of Cardiac

Excitation Using Hardware-Implemented Cardiac

Excitation Modeling. International Journal of

Integrated Engineering, Vol 4, No 3: 13-18,( 2012).

[4] Hodgkin A.L. and Huxley A.F. A Quantitative Description of Membrane Current and Its

Application to Conduction and Excitation in Nerve.

J. Physiol., Vol 117 (1952): 500-544.

[5] Fitzhugh R. Thresholds and Plateaus in the

Hodgkin-Huxley Nerve Equations. J.Gen. Physiol.,

Vol 43, No 5 (1960): 867-896.

[6] Noble D. Cardiac Action Potential and Pacemaker

Potentials Based on the Hodgkin-Huxley Equations.

Nature, Vol 188 (1960): 495-497.

[7] Luo C.H. and Rudy Y. A Model of the Ventricular

Cardiac Action Potential. Depolarization, Repolarization, and Their Interaction. Circulation

Research, Vol 68, No 6 (1991): 1501-1526.

[8] Beeler G.W. and Reuter H. Reconstruction of the

Action Potential of Ventricular Myocardial Fibres. J.

Physiol., Vol 268 (1977): 177-210.

[9] Luo C.H and Rudy Y.A. Dynamic Model of the

Cardiac Ventricular Action Potential. I. Simulations

of Ionic Currents and Concentration Changes. Circ.

Res., Vol 74 (1994): 1071-1096.

[10] Luo C.H. and Rudy Y.A. Dynamic Model of the

Cardiac Ventricular Action Potential. II. After Depolarizations, Triggered Activity, and

Potentiation. Circ. Res., Vol 74 (1994): 1097-1113.

[11] Harmon L.D. Studies with Artificial Neurons, I:

Properties and Functions of an Artificial Neuron.

Kybernetik, Vol 1, No 3 (December 1961): 89-101.

[12] Nagumo J., Arimoto S. and Yoshizawa S. An Active

Pulse Transmission Line Simulating Nerve Axon.

Proceedings of the IRE, Vol 50, No 10 (October

1962): 2061 -2070.

[13] Nagumo J., Yoshizawa S. and Arimoto S. Bistable

Transmission Lines. IEEE Transactions on Circuit

Theory, Vol 12, No 3 (September 1965): 400-412.

[14] Hoshimiya N., Yoshida S., Shogen K. and Matsuo

T. Two-Terminal Electronic Circuit Neuron Model

with Excitable Membrane V–I–T Characteristics

Improvement and Application. Biol. Cybernetics,

Vol 35 (1979): 125-130.

[15] Yagi H. Special Articles on Biomedical Electronics. 1. Biological Cybernetics and Electronics (in

Japanese). Transactions of the Institute of

Electronics. Information and Communication

Engineers, Vol 75, No 9: 916-920, (1992).

BioSystems, Vol 58 (2000): 93-100.

[16] Maeda Y. and Makino H. A Pulse-Type Hardware

Neuron Model with Beating, Bursting Excitation and

Plateau Potential. BioSystems, Vol 58 (2000): 93-

100.

[17] Maeda Y., Yagi E. and Makino H. Synchronization

with Low Power Consumption of Hardware Models

of Cardiac Cells. BioSystems, Vol 79 (2005): 125-131.

[18] Sekine Y., Torita K., Matsuoka J. and Yagi E. Type

Hardware Neuron Model with CMOS IC.

Electronics and Communications in Japan, Part 2,

Vol 85, No 3 (2002): 23-29.

[19] Saeki K., Sekine Y. and Aihara K. Pulse-Type

Bursting Neuron Model using Enhancement Mode

MOSFETs. Electronics and Communications in

Japan, Part 2, Vol 85, No 11 (2002): 1-7.

[20] Mahmud F., Shiozawa N., Makikawa M. and

Nomura T. Reentrant Excitation in an Analog-Digital Hybrid Circuit Model of Cardiac Tissue.

American Institute of Physics, Chaos, Vol 21

(2011): 023121.

[21] Fasih A., Schwarzlmuller C., Chedjou C.J. and

Kyamakya K. Framework for FPGA based Real-

Time Machine. Vision Direct Convolution Versus

CNN ISAST Transactions on Electronics and Signal

Processing, Vol 1, No 4 (2010): 1-76.

[22] Das J., Lam A. and Steven J. E. Wilton. An

Analytical Model Relating FPGA Architecture to

Logic Density and Depth. IEEE Transactions on

Very Large Scale Integration (VLSI) Systems, Vol 19, No 12 (2011): 2229-2242.

[23] Sachin B. Jadhav and Nikhil N. Mane. A Novel

High Speed FPGA Architecture for FIR Filter

Design. International Journal of Reconfigurable and

Embedded Systems (IJRES), Vol 1, No 1 (2012): 1-

10.

[24] Rubin R. Aliev and Alexander V. Panfilov. A

Simple Two Variable Model of Cardiac Excitation.

Chaos Solitons and Fractals, Vol 7 (1996): 293-301.

[25] Nomura T. and Glass L. Entrainment and

Termination of Reentrant Wave Propagation in a Periodically Stimulated Ring of Excitable Media.

Physical Review E., Vol 53, No 6 (1996): 6353-

6360.

Proc. of Microelectronics & Nanotechnology (2014)

7

[26] R. Naderi, M.J. Yazdanpanah, Azemi A. and B.

Nazem R. Tracking Normal Action Potential Based

on the FHN Model Using Adaptive Feedback

Linearization Technique, (2010) 1458-1463.

[27] Lin C.H. and Lin G.W. FPGA Implementation of

Fractal Patterns Classifier for Multiple Cardiac Arrhythmias Detection. J. Biomedical Science and

Engineering, Vol 7 (2012): 120-132,.

[28] Comtois P. and Vinet A. Resetting and Annihilation

of Reentrant Activity in a Model of a Model of a

One-dimensional Loop of Ventricular Tissue. Chaos,

Vol 12, No 3 (2002): 903-922.